Battery/Alternator problem??????

I have a 2000 silverado ext 4x4 5.3l that I have been having a little
problem with.

A few days ago I was driving and noticed the battery light come on and
the volts gauge was reading around 10 -11volts. I turned off all
accessories and headed her for home.

Once home I took the battery (delco factory) to Canadian tire for them
to test it. It tested ""replace". So I did with a new 875cca terminator
battery. When I installed the new battery the truck started fine but I
noticed the battery warning light was still on. I let it run for 20min
or so to see if it would charge. (or what ever was wrong might
magically fix itself) The light didnt go out so I tried some of the
accessories to put a load on it. The wipers and blower motor ran but
noticeably slowly.

I just decided to let the truck run with all accessories off. The
battery light didn't go out so after running for 1/2 hour or so I shut
off the truck and the the battery now shows 11.7V across the terminals.

I charged the battery back up to show 12.6V across the terminals.

Then I started the truck and checked the voltage across the terminals
with the truck running (no access on at all)......11.3V....What
the.....and the bleeping battery warning light is still on.

I tried revving the truck to 2000-2200 rpm (no access on at all) and
the voltage across the battery went up to 11.49 at one point but it
also fluctuated down to 11.27 also....

Does this sound like a new alternater to go along with my new
battery???? What are the odd that both the battery and alternator would
crap on the same day???